@Josh -
On reflection, you should take your grandpa to a camera shop and have him try out a couple of lenses (including the kit ones) to see if the pictures are coming out blurry. That will eliminate the possibility of an equipment problem, and also settle whether he has steady enough hands to take a telephoto picture without some type of device. It also gives him a good idea of what different lenses weigh.
Another thing to keep in mind is that the pictured lens is an 18-55 III. That is not an image stabilized lens, so getting something like a 55-250 IS or IS STM might just do the trick.
At that point, before you pull the trigger, you need to figure out what you're willing to give up, because every lens purchase is a compromise. If you use a "consumer" lens, it will weigh less and perhaps that will allow your grandpa to shoot without a tripod, but he'll be shooting with smaller aperture, which means high ISO (grainier pictures) or slower shutter speeds (maybe blurry). If you buy a higher end lens, the image quality and aperture size go way up, but you're usually looking at much more weight -- even the new, non-L 70-300 nano USM feels a lot heavier than 55-250, nevermind the L series options. And of course, there's price, and availability, especially if you're only looking at used; some are very plentiful, others are rare finds, or at least, the deals are rare finds.
There seems to be some resistance to tripod (or monopod) shooting here, but I maintain that it's a great way to take excellent bird pictures without spending a lot of money. At the expense of lugging around another piece of gear, it allows you to shoot at low ISOs (100, 200) and slower shutter speeds. Depending on the bird you're shooting, sometimes, you don't want crazy high shutter speeds, because a bit of blur in the right place conveys motion (like a hummingbird), and the lowest possible ISO is always preferable.
If you're just hiking and shooting birds along the way, a tripod probably isn't the way to go. But if you're going to a specific place and setting up to shoot a specific bird, it could be. And if you're shooting them from your own home, I think it's definitely something to consider.